<p>A self-similar solution of the linearised magnetohydrodynamic equations describing the propagation of the Alfvén pulse in an axially symmetric magnetic tube of variable diameter is obtained. The electric field component induced by the non-linear Alfvén wave and directed along the tube surface, i.e., accelerating particles along the magnetic field, is determined on the basis of the perturbation theory and specified to the case of a magnetic flux tube homogeneous over its cross-section. For the chromospheric tubes, whose configuration is given by the barometric law of plasma pressure decrease, the conditions for achieving the super-Dreicer electric field limit necessary to drive the accelerated high-energy electrons into the coronal part of the loop are established.</p>